An automatic balance crane can vary the counterweight position as the load radius changes. This conceptual animation shows a load trolley on one side of a mast and a moving counterweight on the other. Use the calculator to compare the two ideal moments and the moment change associated with a hook-radius position error.
Automatic Balance Crane Interactive Calculator
Compare hook-load moment, ideal balancing moment and a simple position-error estimate. The 2% comparison band is an example setting, not an allowable crane rating.
Equation Used
Hook load times horizontal radius gives a load moment in tonne-force meters. The calculator sets Counter-Moment equal to that value. Lag Error is hook weight times the entered equivalent hook-radius error; it does not simulate a control response.
- Tonnes are treated as tonne-force for tonne-metre moment calculations.
- Counter-moment is set equal to load moment as an ideal balance condition.
- Lag Error uses hook weight and an equivalent hook-radius mismatch, not counterweight travel error.
- The 2% band is an illustrative fraction of Reference moment, not an operating limit.
The drawing uses an illustrative counterweight twice the hook mass, so it travels half the hook radius. It does not model boom weight, stability, structural capacity or a particular commercial crane.
Moving the counterweight to follow the load
A vertical load produces a moment equal to its weight times horizontal distance from the chosen reference axis. A counterweight on the opposite side produces a moment in the opposite direction. For the two contributions alone to cancel, W_c R_c = W R.
The animation uses a counterweight twice the hook mass. Its radius is therefore half the hook radius. As the load trolley travels from half to full entered reach, the counterweight moves proportionally on the other side. The numerical tiles describe full entered reach rather than the changing illustrated position.
What to identify
- Hook and load trolley: set the displayed load position.
- Main jib: carries the trolley path.
- Counter-jib and ballast trolley: show the opposite balancing moment.
- Mast and support: carry the vertical loads.
The drawing demonstrates a geometric relationship. It does not represent a named commercial crane or show an actual drive, sensor specification or load-moment limiter. Even when these two moments cancel, the support still carries forces and the members still carry internal loads.
Understanding a variable-radius load
A moving counterweight can vary one contribution to the total moment as a load moves. The example is useful for studying why both weight and reach matter and why changing the counterweight mass changes the distance required for balance.
A complete crane assessment also includes jib and machinery weight, the support arrangement, wind, acceleration, deflection, structural strength and stability. Moment balance between two ideal point loads alone cannot establish lift capacity, foundation size or bearing life.
Use the actual crane’s approved configuration and load chart for lifting decisions. This educational diagram does not authorize added ballast, changed travel limits, controller tuning or operation from a floating platform.
The four calculator values
Load Moment = W × R and Counter-Moment = Load Moment. Here W is the entered hook load expressed in metric tonnes, treated numerically as tonne-force, and R is horizontal radius in meters. The displayed tm therefore means tonne-force meters; 1 tf·m corresponds to 9.80665 kN·m at standard gravity.
Lag Error = W × e/1000, where e is Position Lag in millimeters. This is the moment magnitude associated with an equivalent error in hook radius. It is not a predicted dynamic lag, and it is not the same as W_c times an actual counterweight-position error.
Example 2% band = 0.02 × Reference moment. The reference input has no effect on the computed load or counter-moment. The 2% multiplier is an illustration, not a crane-code allowance, bearing limit or approval threshold.
For a separately chosen counterweight W_c, the ideal two-load balance radius is R_c = WR/W_c. In the drawing W_c = 2W, so R_c = R/2. Changing hook load also changes that illustrative counterweight mass; there is no independently entered fixed ballast or travel limit.
Worked example: two equal moments
At the initial settings, W = 5 t, R = 40 m, e = 150 mm and Reference moment = 280 tm. Load Moment is 200 tf·m, and the assumed Counter-Moment is also 200 tf·m. Lag Error is 5 × 0.150 = 0.75 tf·m. The example band is 0.02 × 280 = 5.6 tf·m.
At full reach the drawing uses an illustrative 10 t counterweight at 20 m. Its moment equals the 5 t hook load at 40 m. When the illustrated hook reaches 20 m, the counterweight reaches 10 m; each moment is then 100 tf·m, while the result tiles still refer to full reach.
Changing only R to 20 m makes each full-reach moment 100 tf·m but leaves Lag Error at 0.75 and the band at 5.6. Changing only the reference value to 500 tm makes the band 10 tf·m and leaves the other results unchanged.
If an actual 10 t counterweight were displaced 150 mm from its balancing position, its moment error would be 1.5 tf·m. That differs from the tile’s 0.75 tf·m because the tile multiplies the entered distance by hook weight. None of these comparisons evaluates whether a lift is permissible.
Balance and capacity answer different questions
| Question | What this model provides |
|---|---|
| How does reach affect hook moment? | Moment changes in direct proportion to radius. |
| Where would a chosen counterweight balance two loads? | The relation R_c = WR/W_c, with other moments omitted. |
| What does position error contribute? | Weight times the error distance for the specified load. |
| Is a crane stable and strong enough? | That requires the full machine and operating configuration, beyond this model. |
The drawing does not predict controller overshoot, stopping time, encoder accuracy or fail-safe behavior.
Counterweight-balance questions
No. Equality is imposed for two ideal loads. Real stability and structural capacity require the complete crane configuration and loading.
An equivalent hook-radius error. The tile multiplies that distance by hook weight; it does not simulate delayed counterweight motion.
Not as the same physical quantity when counterweight and hook weights differ. Counterweight error produces W_c times its displacement; this tile uses W.
No. It is an illustrative proportion of an entered reference moment and does not determine allowable operation.
They use the full entered radius. The animation separately illustrates travel between half and full reach.
The illustration always sets counterweight mass to twice hook mass, so its balancing radius remains half the hook radius.
No. A real ballast configuration must account for the whole crane and its approved design; this two-load illustration is not a modification instruction.
No. It compares static moments and a geometric position-error term, with no dynamic or wind-force calculation.
Statics reference
OpenStax, Conditions for Static Equilibrium, explains the force and moment balance conditions used to interpret the example.
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